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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.analysis.integration.gauss;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import org.apache.commons.math3.analysis.UnivariateFunction;<a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math3.exception.DimensionMismatchException;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.exception.NonMonotonicSequenceException;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.util.MathArrays;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.util.Pair;<a name="line.23"></a>
<FONT color="green">024</FONT>    <a name="line.24"></a>
<FONT color="green">025</FONT>    /**<a name="line.25"></a>
<FONT color="green">026</FONT>     * Class that implements the Gaussian rule for<a name="line.26"></a>
<FONT color="green">027</FONT>     * {@link #integrate(UnivariateFunction) integrating} a weighted<a name="line.27"></a>
<FONT color="green">028</FONT>     * function.<a name="line.28"></a>
<FONT color="green">029</FONT>     *<a name="line.29"></a>
<FONT color="green">030</FONT>     * @since 3.1<a name="line.30"></a>
<FONT color="green">031</FONT>     * @version $Id: GaussIntegrator.java 1382197 2012-09-07 22:35:01Z erans $<a name="line.31"></a>
<FONT color="green">032</FONT>     */<a name="line.32"></a>
<FONT color="green">033</FONT>    public class GaussIntegrator {<a name="line.33"></a>
<FONT color="green">034</FONT>        /** Nodes. */<a name="line.34"></a>
<FONT color="green">035</FONT>        private final double[] points;<a name="line.35"></a>
<FONT color="green">036</FONT>        /** Nodes weights. */<a name="line.36"></a>
<FONT color="green">037</FONT>        private final double[] weights;<a name="line.37"></a>
<FONT color="green">038</FONT>    <a name="line.38"></a>
<FONT color="green">039</FONT>        /**<a name="line.39"></a>
<FONT color="green">040</FONT>         * Creates an integrator from the given {@code points} and {@code weights}.<a name="line.40"></a>
<FONT color="green">041</FONT>         * The integration interval is defined by the first and last value of<a name="line.41"></a>
<FONT color="green">042</FONT>         * {@code points} which must be sorted in increasing order.<a name="line.42"></a>
<FONT color="green">043</FONT>         *<a name="line.43"></a>
<FONT color="green">044</FONT>         * @param points Integration points.<a name="line.44"></a>
<FONT color="green">045</FONT>         * @param weights Weights of the corresponding integration nodes.<a name="line.45"></a>
<FONT color="green">046</FONT>         * @throws NonMonotonicSequenceException if the {@code points} are not<a name="line.46"></a>
<FONT color="green">047</FONT>         * sorted in increasing order.<a name="line.47"></a>
<FONT color="green">048</FONT>         */<a name="line.48"></a>
<FONT color="green">049</FONT>        public GaussIntegrator(double[] points,<a name="line.49"></a>
<FONT color="green">050</FONT>                               double[] weights)<a name="line.50"></a>
<FONT color="green">051</FONT>            throws NonMonotonicSequenceException {<a name="line.51"></a>
<FONT color="green">052</FONT>            if (points.length != weights.length) {<a name="line.52"></a>
<FONT color="green">053</FONT>                throw new DimensionMismatchException(points.length,<a name="line.53"></a>
<FONT color="green">054</FONT>                                                     weights.length);<a name="line.54"></a>
<FONT color="green">055</FONT>            }<a name="line.55"></a>
<FONT color="green">056</FONT>    <a name="line.56"></a>
<FONT color="green">057</FONT>            MathArrays.checkOrder(points, MathArrays.OrderDirection.INCREASING, true, true);<a name="line.57"></a>
<FONT color="green">058</FONT>    <a name="line.58"></a>
<FONT color="green">059</FONT>            this.points = points.clone();<a name="line.59"></a>
<FONT color="green">060</FONT>            this.weights = weights.clone();<a name="line.60"></a>
<FONT color="green">061</FONT>        }<a name="line.61"></a>
<FONT color="green">062</FONT>    <a name="line.62"></a>
<FONT color="green">063</FONT>        /**<a name="line.63"></a>
<FONT color="green">064</FONT>         * Creates an integrator from the given pair of points (first element of<a name="line.64"></a>
<FONT color="green">065</FONT>         * the pair) and weights (second element of the pair.<a name="line.65"></a>
<FONT color="green">066</FONT>         *<a name="line.66"></a>
<FONT color="green">067</FONT>         * @param pointsAndWeights Integration points and corresponding weights.<a name="line.67"></a>
<FONT color="green">068</FONT>         * @throws NonMonotonicSequenceException if the {@code points} are not<a name="line.68"></a>
<FONT color="green">069</FONT>         * sorted in increasing order.<a name="line.69"></a>
<FONT color="green">070</FONT>         *<a name="line.70"></a>
<FONT color="green">071</FONT>         * @see #GaussIntegrator(double[], double[])<a name="line.71"></a>
<FONT color="green">072</FONT>         */<a name="line.72"></a>
<FONT color="green">073</FONT>        public GaussIntegrator(Pair&lt;double[], double[]&gt; pointsAndWeights)<a name="line.73"></a>
<FONT color="green">074</FONT>            throws NonMonotonicSequenceException {<a name="line.74"></a>
<FONT color="green">075</FONT>            this(pointsAndWeights.getFirst(), pointsAndWeights.getSecond());<a name="line.75"></a>
<FONT color="green">076</FONT>        }<a name="line.76"></a>
<FONT color="green">077</FONT>    <a name="line.77"></a>
<FONT color="green">078</FONT>        /**<a name="line.78"></a>
<FONT color="green">079</FONT>         * Returns an estimate of the integral of {@code f(x) * w(x)},<a name="line.79"></a>
<FONT color="green">080</FONT>         * where {@code w} is a weight function that depends on the actual<a name="line.80"></a>
<FONT color="green">081</FONT>         * flavor of the Gauss integration scheme.<a name="line.81"></a>
<FONT color="green">082</FONT>         * The algorithm uses the points and associated weights, as passed<a name="line.82"></a>
<FONT color="green">083</FONT>         * to the {@link #GaussIntegrator(double[],double[]) constructor}.<a name="line.83"></a>
<FONT color="green">084</FONT>         *<a name="line.84"></a>
<FONT color="green">085</FONT>         * @param f Function to integrate.<a name="line.85"></a>
<FONT color="green">086</FONT>         * @return the integral of the weighted function.<a name="line.86"></a>
<FONT color="green">087</FONT>         */<a name="line.87"></a>
<FONT color="green">088</FONT>        public double integrate(UnivariateFunction f) {<a name="line.88"></a>
<FONT color="green">089</FONT>            double s = 0;<a name="line.89"></a>
<FONT color="green">090</FONT>            double c = 0;<a name="line.90"></a>
<FONT color="green">091</FONT>            for (int i = 0; i &lt; points.length; i++) {<a name="line.91"></a>
<FONT color="green">092</FONT>                final double x = points[i];<a name="line.92"></a>
<FONT color="green">093</FONT>                final double w = weights[i];<a name="line.93"></a>
<FONT color="green">094</FONT>                final double y = w * f.value(x) - c;<a name="line.94"></a>
<FONT color="green">095</FONT>                final double t = s + y;<a name="line.95"></a>
<FONT color="green">096</FONT>                c = (t - s) - y;<a name="line.96"></a>
<FONT color="green">097</FONT>                s = t;<a name="line.97"></a>
<FONT color="green">098</FONT>            }<a name="line.98"></a>
<FONT color="green">099</FONT>            return s;<a name="line.99"></a>
<FONT color="green">100</FONT>        }<a name="line.100"></a>
<FONT color="green">101</FONT>    <a name="line.101"></a>
<FONT color="green">102</FONT>        /**<a name="line.102"></a>
<FONT color="green">103</FONT>         * @return the order of the integration rule (the number of integration<a name="line.103"></a>
<FONT color="green">104</FONT>         * points).<a name="line.104"></a>
<FONT color="green">105</FONT>         */<a name="line.105"></a>
<FONT color="green">106</FONT>        public int getNumberOfPoints() {<a name="line.106"></a>
<FONT color="green">107</FONT>            return points.length;<a name="line.107"></a>
<FONT color="green">108</FONT>        }<a name="line.108"></a>
<FONT color="green">109</FONT>    }<a name="line.109"></a>




























































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